The present invention relates to a clamp-on type ultrasonic flow meter and a method of compensating for influences exerted by temperature and pressure of a fluid and by temperature of a detector in an ultrasonic flow meter for measuring a flow velocity or a flow amount of a fluid based on a difference in propagation time of ultrasonic waves through the fluid caused by a flow of the fluid, and more particularly, to such a compensation method for use in a clamp-on type ultrasonic flow meter having ultrasonic transducers closely attached on an outer wall surface of an existing pipe for measuring a flow velocity of a fluid flowing through the pipe.
When ultrasonic waves propagate through a flowing fluid, the ultrasonic waves are affected by the fluid flow so that a propagation time measured when the ultrasonic waves are directed from the upstream side to the downstream side of the fluid flow is different from that measured when directed from the downstream side to the upstream side of the fluid flow. Since the difference in the propagation time is in a proportional relationship with the flow velocity of the fluid, an ultrasonic flow meter utilizes this relationship for measuring the flow velocity of the fluid.
In plant facilities for water treatment, iron manufacturing, chemical processing, district air conditioning, and the like, liquids such as water, corrosive fluids and the like are supplied through pipes. If a flow amount of a fluid flowing through an existing pipe needs to be measured, a clamp-on type ultrasonic flow meter may be employed, wherein a pair or more of ultrasonic transducers are mounted closely on the outer wall surface of the existing pipe such that ultrasonic waves are transmitted and received through the pipe wall to measure the flow amount of the fluid flowing through the pipe.
FIGS. 6A and 6B illustrate a basic configuration of a detector unit of a clamp-on type ultrasonic flow meter. First, the principle of the ultrasonic flow meter for measuring a flow velocity of a fluid will be explained with reference to FIGS. 6A, 6B. FIG. 6A illustrates the whole configuration of the detector unit, and FIG. 6B illustrates in greater detail an ultrasonic transducer mounting member.
A detector unit 100 of the clamp-on type ultrasonic flow meter illustrated in FIG. 6A includes ultrasonic oscillators 1a, 1b, and oblique wedges 2a, 2b for acoustically coupling a fluid 4 flowing in a pipe 3 to the ultrasonic oscillators 1a, 1b. The ultrasonic oscillators and the oblique wedges are acoustically coupled to constitute ultrasonic transducers 10a, 10b.
When a driving pulse is applied to the ultrasonic oscillator 1a of the upstream ultrasonic transducer 10a in the detector unit 100 of the ultrasonic flow meter for causing the ultrasonic oscillator la to oscillate, ultrasonic waves are emitted therefrom and propagate through the oblique wedge 2a and the pipe 3 to the fluid 4 flowing in the pipe 3. Then, the ultrasonic waves propagating through the fluid 4 in the pipe reach the opposite wall of the pipe 3, and then are guided by the oblique wedge 2b, lead by the ultrasonic transducer 10b, now set in a receiver mode, and received by the ultrasonic oscillator 1b.
The ultrasonic waves emitted from the ultrasonic oscillator 1a are elastic waves having a certain spreading and directivity. However, it is a general tendency that an ultrasonic wave source and a receiver unit are regarded as points at the center of the elastic waves and a propagation path of the wave front is treated as an acoustic line passing through these two points. In this event, at a location in a propagation medium where sonic speed changes discontinuously, a law of reflection and refraction is satisfied with respect to the propagation of wave motion. Such a model is generally referred to as a point sound source model.
In the following, an analysis will be made on a process of the propagation of ultrasonic waves in the detector unit 100 of the clamp-on type ultrasonic flow meter configured as illustrated in FIG. 6, on the basis of the point sound source model, in order to explain the relationship between a propagation time of ultrasonic waves propagating from one ultrasonic transducer to the other and a flow velocity of a fluid flowing through the pipe on which the detector unit is installed.
Assuming that T.sub.1 represents a forward direction propagation time of ultrasonic waves emitted from the upstream ultrasonic transducer 10a and reaching the downstream ultrasonic transducer 10b, and T.sub.2 represents a backward direction propagation time of the ultrasonic waves emitted from the downstream ultrasonic transducer 10b and received by the upstream ultrasonic transducer 10a, the propagation times T.sub.1, T.sub.2 are given by the following Equations (1) and (2), respectively, which express that a propagation distance of the ultrasonic waves is divided by effective sonic speed, i.e., the sum of sonic speed and a component of a flow velocity of the fluid in the ultrasonic wave propagating direction:
Equation (1)! EQU T.sub.1 =(D/cos.theta..sub.f)/(C.sub.f +V sin.theta..sub.f)+.tau.(1)
Equation (2)! EQU T.sub.2 =(D/cos.theta..sub.f)/(C.sub.f -V sin.theta..sub.f)+.tau.(2)
where
D: a distance between opposite inner wall surfaces of the pipe through which the ultrasonic waves pass (inner diameter if the pipe has a circular shape in cross-section); PA0 .tau.: a propagation time of the ultrasonic waves passing through the pipe and the oblique wedges; PA0 C.sub.f : sonic speed in the fluid; PA0 V: an average flow velocity of the fluid on sound rays; and PA0 .theta.f: a refraction angle of the ultrasonic waves from the pipe to the fluid.
Thus, a difference .DELTA.T between the forward and backward propagation times T.sub.1 and T.sub.2 is first given by the following Equation (3a). However, when a fluid under measurement is water, sonic speed C.sub.f is approximately 1,500 m/s whereas the flow velocity V of the fluid in the pipe rarely exceeds 30 m/s at the highest, so that C.sub.f.sup.2 &gt;&gt;V.sup.2 stands, and therefore an approximation expressed by Equation (3b) is satisfied at very high accuracy:
Equation (3)! ##EQU1##
By substituting zero for the flow velocity V of a fluid in Equation (1) or Equation (2), a propagation time T.sub.0 of the fluid in a stationary state is given by Equation (4). On the other hand, by adding Equation (1) to Equation (2) and applying the approximation of the relationship between sonic speed C.sub.f in the fluid and the fluid flow velocity V to the addition result, Equation (5) is derived in the same form as Equation (4). As a result, the propagation time T.sub.0 of the fluid at a stationary state may be approximated by an average value of measured propagation times of ultrasonic waves in the forward and backward directions, detected between the ultrasonic transducers 1a, 1b of the detector unit 100 of the ultrasonic flow meter when the fluid is flowing.
Equation (4)! EQU T.sub.0 =(D/cos.theta..sub.f)/C.sub.f +.tau. (4)
Equation (5)! ##EQU2##
By substituting C.sub.f from Equation (3b) and Equation (4), Equation (6) expressing an average flow velocity on sound rays of the fluid in the pipe is derived:
Equation (6)! EQU V=(D/sin2.theta..sub.f){.DELTA.T/(T.sub.0 -.tau.).sup.2 } (6)
The propagation time difference .DELTA.T and the propagation time T.sub.0 of the fluid in a stationary state may be derived by an approximation based on measured values detected by the detector unit 100 of the ultrasonic flow meter when the fluid is flowing, as explained above.
On the other hand, between an incident angle .theta..sub.f of sound rays into the fluid and the propagation time .tau. of ultrasonic waves through the pipe and the oblique wedges, the relationship explained below is satisfied based on the law of reflection and refraction with respect to the propagation of wave motion.
More specifically, as illustrated in FIG. 6B which is a detailed explanatory diagram of a mounting member for the ultrasonic transducer, assuming:
t.sub.w : a length of sound rays in the oblique wedge projected onto a plane perpendicular to the center axis of the pipe; PA1 t.sub.p : a thickness of the wall of a pipe; PA1 C.sub.w : sonic speed in the material of the oblique wedge; PA1 C.sub.p : sonic speed in the material of the pipe; PA1 .theta..sub.w : an incident angle of sound rays from the oblique wedge to the pipe; PA1 .theta..sub.p : a refraction angle of ultrasonic waves from the oblique wedge to the pipe (i.e., an incident angle of sound rays from the pipe to a fluid); PA1 .theta..sub.r : a refraction angle of the ultrasonic waves from the pipe to the fluid,
Equation (7) is satisfied based on the law of refraction with respect to the propagation of wave motion at respective interfaces between propagation media of the oblique wedge 2, the pipe 3, and the fluid 4, and a ratio C of sonic speed to the refraction angle ratio (hereinafter, this ratio is called the sonic speed/refraction angle ratio) on the right side is a constant in accordance with the law of refraction.
Equation (7)! EQU C.sub.w /sin.theta..sub.w =C.sub.p /sin.theta..sub.p =C.sub.f /sin.theta..sub.f =C (constant) (7)
The propagation time .tau. of ultrasonic waves through the pipe 3 and the oblique wedges 2 is expressed by the following Equation (8) which means the sum of the propagation times of the ultrasonic waves on the transmission and reception sides, since the ultrasonic waves pass through these elements on the respective sides.
Equation (8)! EQU .tau.=2t.sub.w /(C.sub.w cos.theta..sub.w)+2t.sub.p /(C.sub.p cos.theta..sub.p) (8)
In Equation (7), the sonic speed values C.sub.w, C.sub.p, C.sub.f in the respective media can be previously derived by a search, once service conditions are established for materials used for members such as the oblique wedges 2 and the pipe 3, the kind and temperature of a fluid flowing through the pipe 3, and so on. Also, since the incident angle .theta..sub.w of sound rays from the oblique wedge 2 to the pipe 3 has been determined in the design of the oblique wedge 2, the refraction angle .theta..sub.p of sound rays from the oblique wedge 2 to the pipe 3 and the refraction angle .theta..sub.f of sound rays from the pipe 3 to the fluid can be derived by applying the known values into Equation (7).
Further, the projection length t.sub.w of sound rays in the oblique wedge 2 projected onto a plane perpendicular to the center axis of the pipe has been determined in the design of the oblique wedge 2, and the distance D between opposite inner wall surfaces and the thickness t.sub.p of the pipe are also data which is previously obtainable from the standard of pipes or from actual measurements.
The values of the propagation time difference .DELTA.T and the propagation time T.sub.0 of the fluid in a stationary state, derived by an acoustic measurement by the detector unit of the ultrasonic flow meter, associated design values of the detector unit, the incident angle .theta..sub.f of sound rays from the pipe to the fluid, determined by the kind of the fluid flowing through the pipe, and the propagation time .tau. of the ultrasonic waves through the pipe and the oblique wedge are substituted into Equation (6) to derive an average flow velocity V on sound rays of the fluid flowing through the pipe on which the detector unit is installed. A flow amount of the fluid in a pipe having a circular shape in cross-section, for example, is calculated by Equation (9):
Equation (9)! EQU Q=(.pi.D.sup.2 /4)(1/K)(D/sin2.theta..sub.f){.DELTA.T/(T.sub.0 -.tau.).sup.2 } (9)
K in Equation (9) is a conversion coefficient for the conversion between an average flow velocity on sound rays in the fluid and an average flow velocity on the cross section of the pipe.
The measurement principle of the clamp-on type ultrasonic flow meter has been described hereinabove. For actual installation of the ultrasonic flow meter, the ultrasonic transducers may be mounted on opposite sides of the fluid pipe 3 such that a propagation path of ultrasonic waves forms a Z-shape, as illustrated in the principle explaining diagram of FIG. 6A, or the ultrasonic transducers may be mounted on the same side on the outer wall surface of the pipe to form a propagation path of ultrasonic waves in a V-shape such that ultrasonic waves emitted from one ultrasonic transducer and reflected by the inner wall surface of the pipe is received by the other ultrasonic transducer mounted on the same side, as illustrated in FIG. 7.
When the ultrasonic transducers are mounted on the same side on the outer wall surface of the fluid pipe, as illustrated in FIG. 7, ultrasonic waves are emitted from one ultrasonic transducer, reciprocate in the diametrical direction of the pipe, and are received by the other ultrasonic transducer. Thus, the relationship between propagation times T.sub.1, T.sub.2 and the flow velocity V is given by substituting 2D into the distance D between the opposite inner wall surfaces in Equations (1) and (2). It will be understood from this fact that the configuration of the two ultrasonic transducers on the same side is regarded as completely the same as the configuration of those illustrated in FIG. 6 in terms of the principles.
A propagation speed C.sub.f of ultrasonic waves propagating a medium as vertical waves has a relationship with the density .rho. and the volumetric elasticity .kappa. of the medium expressed by the following Equation (10).
Equation (10)! ##EQU3##
Since the density .rho. and the volumetric elasticity .kappa. of the medium in Equation (10) vary depending on temperature and pressure of the medium, the propagation speed C.sub.f of ultrasonic waves in the medium also exhibits temperature and pressure dependency. If the medium is gas, its temperature and pressure are in a relationship expressed by the gas state equation.
While the propagation speed C.sub.f of ultrasonic waves in a liquid also exhibits dependency for temperature and pressure, there is no simple equation expressing a relationship which is commonly satisfied irrespective of the kind of liquids, as the gas state equation. Thus, actual measurements have been made for representative particular liquid materials to obtain data associated with the relationship.
A simplified state diagram for water, which has been most frequently applied to obtain the above relationship of liquid, is shown in FIG. 8. It should be noted that this diagram is quoted from the steam tables published by Japan Society of Mechanical Engineers (1980).
As can be seen from FIG. 8, when water temperature is gradually raised from the vicinity of 0.degree. C., sonic speed in water also rises to approximately 70.degree. C., exhibits a maximum value in the vicinity of 75.degree. C., and then begins to decrease. Stated another way, water temperature is a two-valued function of sonic speed in water, so that sonic speed in water exhibits the same value at different two temperature levels. Also, as the pressure is increased, sonic speed in water also increases, so that sonic speed in water has larger dependency for pressure in a higher temperature range.
Although not so remarkable as sonic speed in liquid, sonic speed in solid materials, respectively constituting the oblique wedges and the pipe wall, also exhibits temperature dependency. Generally, as the temperature is raised, sonic speed in these materials decreases, as shown in FIG. 9.
As explained above, since sonic speed of ultrasonic waves propagating not only a liquid flowing through a pipe of a clamp-on type ultrasonic flow meter but also the oblique wedges and the pipe wall constituting the detector unit of the flow meter exhibits the temperature dependency, measurement errors and variations in output will be remarkable unless measured values of sonic speed are subjected to compensation for temperature and/or pressure, if temperature and/or pressure of the liquid vary or temperature of the oblique wedges and the pipe varies due to the action of liquid temperature and environmental temperature.
Since an average value T.sub.0 of the propagation times in the forward and backward directions and sonic speed in liquid is in the relationship expressed by Equation (5) when the liquid pressure is held constant. Thus, for a liquid with a known relationship between sonic speed and temperature, if an average value T.sub.0 of the propagation times of ultrasonic waves through the liquid in the forward and backward directions is measured, the temperature of the liquid can be derived from the measured value through the sonic speed, thus providing additionally the value of a temperature change ratio of sonic speed under the measuring conditions. Using a function expressing this relationship, when an average value T.sub.0S of propagation times measured at reference pressure and temperature levels is designated a reference for the propagation time, the relationship between a difference of an average value T.sub.0 of the propagation times from the reference value T.sub.0S and sonic speed in a liquid, i.e., the relationship between the difference (T.sub.0 -T.sub.0s) and a refraction angle .theta..sub.f can be previously derived from Equation (7). Thus, in a conventional clamp-on type ultrasonic flow meter, the relationship between a difference portion of a propagation time average value T.sub.0 from the reference value T.sub.0S and a refraction angle .theta..sub.f or a change amount of its trigonometric function are stored in a flow velocity calculation unit, such that upon detecting a change in the propagation time average value T.sub.0, sonic speed in a fluid under measuring conditions can be calculated based on the stored data in the flow velocity calculation unit to derive a temperature compensated flow velocity value.
For pressure compensation, on the other hand, a pressure sensor is separately provided for measuring fluid pressure of a liquid having a known relationship between sonic speed and pressure, such that sonic speed is corrected based on a detected pressure value of the pressure sensor.
In the conventional clamp-on type ultrasonic flow meter as described in the previous paragraph, if the relationship between sonic speed and pressure is not known for a fluid under measurement, it is impossible to correct measurement errors due to changes in pressure and variations in output caused by fluctuations in pressure. In addition, even if the relationship between sonic speed and pressure is known, a pressure sensor must be provided for measuring a fluid pressure to correct the sonic speed in terms of pressure based on the measured value.
Also, for a fluid under measurement exhibiting a large temperature change, a temperature correction may be carried out to provide more accurate measured values, only when the relationship between sonic speed in the fluid under measurement and temperature is previously known. However, if the relationship between sonic speed and temperature is unknown, an appropriate temperature correction cannot be made for providing highly accurate measured values.
Moreover, even if the relationship between sonic speed in the fluid and the temperature is known, means for measuring fluid temperature or a physical amount equivalent to the fluid temperature is required to correct sonic speed in terms of temperature based on a measured value from the measuring means. Particularly, when measuring a fluid such as water in which sonic speed exhibits a maximum value and has temperature dependency largely differing on one and the other sides of the maximum value, a correction region must be determined based on a detected temperature value of the fluid under measurement to modify compensation coefficients.
Further, in the prior art, propagation paths of ultrasonic waves through oblique wedges in the ultrasonic transducers and through a pipe material are fixed for convenience, such that a constant value derived from sonic speed over the respective path length in the respective materials at a given temperature is designated a propagation time .tau. of ultrasonic waves through the oblique wedges and the pipe. However, even if sonic speed of ultrasonic waves through the materials of the oblique wedges and the pipe is identical, changes in temperature and/or pressure of the fluid under measurement causes the propagation paths of ultrasonic waves through the oblique wedges and the pipe to change. Also, although not so remarkable as in the case of liquid, sonic speed of ultrasonic waves through the respective solid materials of the oblique wedges and the pipe varies depending on temperature. Generally, as the temperature rises, sonic speed in the respective materials decreases. Thus, variations in temperature and pressure of the fluid, or variations in temperature of the oblique wedges and the pipe due to the action of fluid temperature and environmental temperature will result in measurement errors and variations in output.